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Document embedding

Trained a doc2vec embedding based on skip-gram on the politician level i.e. all tweets of one politician are treated as a document.

\(\Rightarrow\) One obtains a 300 dimensional embedding vector for each politician.

# load necessary functions and embeddings
load(paste0(here::here(), "/doc2vec_graph/politician_level_dco2vec.RData"))
load(paste0(here::here(), "/doc2vec_graph/word_embedding_utils.RData"))
load(paste0(here::here(), "/doc2vec_graph/doc_clust_utils.RData"))
load(paste0(here::here(), "/doc2vec_graph/graph_metrics.RData"))
library(tidyverse)
library(visNetwork)
library(tidygraph)
library(ggraph)
library(patchwork)
# precompute some important quantities
pairwise_doc_sim <- calc_pairwise_doc_sim(document_embedding)
edges <- data.frame(from = pairwise_doc_sim[, 1],
                    to = pairwise_doc_sim[, 2],
                    value = pairwise_doc_sim[, 3],
                    title = paste0(round(pairwise_doc_sim[, 3], 5)))
knn_edges <- create_knn_edges(
  pairwise_doc_similarity = pairwise_doc_sim,
  nodes = nodes,
  k = 5
)


# UWOT
umap_doc_emb <- uwot::umap(
  X = document_embedding,
  n_components = 3,
  approx_pow = TRUE,
  n_epochs = 20
)
colnames(umap_doc_emb) <- c("x", "y", "z")
umap_doc_emb %>%
  as_tibble() %>%
  bind_cols(nodes) %>%
  plotly::plot_ly(x = ~x, y = ~y, z = ~z, color = ~group,
                  colors = c("blue", "black", "darkgrey",
                             "violet", "orange",
                             "green", "red"),
                  marker = list(symbol = "circle",
                                size = 3),
                  text = ~label) %>%
  plotly::add_markers(opacity = 1) %>%
  plotly::layout(
    legend = list(itemsizing = "constant", font = list(size = 15)),
    scene = list(
      xaxis = list(title = ""),
      yaxis = list(title = ""),
      zaxis = list(title = "")
    ),
    title = "Umap dimensionality reduction of politician embedding"
  )

Clustering on the document embedding by party

Apply hierarchical clustering \(\rightarrow\) analyze the dendrograms.

cluster_size <- nodes %>%
  group_by(group) %>%
  summarise(n_cluster = ceiling(n() * 0.3))
afd_clust <- doc_emb_clustering(
  document_embedding = document_embedding,
  nodes = nodes,
  n_cluster = cluster_size$n_cluster[cluster_size$group == "AFD"],
  party = "AFD",
  branch_width = 2
)

fdp_clust <- doc_emb_clustering(
  document_embedding = document_embedding,
  nodes = nodes,
  n_cluster = cluster_size$n_cluster[cluster_size$group == "FDP"],
  party = "FDP",
  branch_width = 2
)

cdu_clust <- doc_emb_clustering(
  document_embedding = document_embedding,
  nodes = nodes,
  n_cluster = cluster_size$n_cluster[cluster_size$group == "CDU"],
  party = "CDU",
  branch_width = 2
)

csu_clust <- doc_emb_clustering(
  document_embedding = document_embedding,
  nodes = nodes,
  n_cluster = cluster_size$n_cluster[cluster_size$group == "CSU"],
  party = "CSU",
  branch_width = 2
)

linke_clust <- doc_emb_clustering(
  document_embedding = document_embedding,
  nodes = nodes,
  n_cluster = cluster_size$n_cluster[cluster_size$group == "Die Linke"],
  party = "Die Linke",
  branch_width = 2
)

gruene_clust <- doc_emb_clustering(
  document_embedding = document_embedding,
  nodes = nodes,
  n_cluster = cluster_size$n_cluster[cluster_size$group == "Grüne"],
  party = "Grüne",
  branch_width = 2
)

spd_clust <- doc_emb_clustering(
  document_embedding = document_embedding,
  nodes = nodes,
  n_cluster = cluster_size$n_cluster[cluster_size$group == "SPD"],
  party = "SPD",
  branch_width = 2
)

Die Grünen

gruene_clust$dendro

umap_cluster_plot(
  document_embedding = document_embedding,
  nodes = nodes,
  cluster_assignments = gruene_clust$cluster_assignments,
  party = "Grüne"
)

SPD

spd_clust$dendro

umap_cluster_plot(
  document_embedding = document_embedding,
  nodes = nodes,
  cluster_assignments = spd_clust$cluster_assignments,
  party = "SPD"
)

Analyse similarities

Calculate pairwise similarities within the document embedding. The resulting similarities can be displayed as a undirected similarity graph with

• Nodes: Politicians
• Edges: Similarities weighted by the computed pairwise similarity

This very dense graph can be represented either in a

• Neighborhood graph: cutoff all edges below a certain similarity threshold
• KNN graph: for each politician keep only all its k highest “outgoing” edges w.r.t. similarity

The graph for each party can be displayed vizually along the cluster assignments that were computed on the document embedding.

AFD

Here the 5-NN Graph is used.

party_graph_docclust(
  party_char = "AFD",
  cluster_assignments = afd_clust$cluster_assignments,
  nodes = nodes,
  edges = knn_edges
)

SPD

Here the 5-NN Graph is used.

party_graph_docclust(
  party_char = "SPD",
  cluster_assignments = spd_clust$cluster_assignments,
  nodes = nodes,
  edges = knn_edges
)

Graph metrics by party

Having these similarity graphs one can use common graph metrics to assess heterogeneity within parties and compare these metrics.

Here the neighborhood graph is used.

metrics_neighboring_graph_0.001$plot

metrics_neighboring_graph_0.001$hop_plot